Significance

Can fish reduce their energy expenditure by schooling? We answer affirmatively this longstanding question by combining state-of-the-art direct numerical simulations of the 3D Navier–Stokes equations with reinforcement learning, using recurrent neural networks with long short-term memory cells to account for the unsteadiness of the flow field. Surprisingly, we find that swimming behind a leader is not always associated with energetic benefits for the follower. In turn, we demonstrate that fish can improve their sustained propulsive efficiency by placing themselves at appropriate locations in the wake of other swimmers and intercepting their wake vortices judiciously. The results show that autonomous, “smart” swimmers may exploit unsteady flow fields to reap substantial energetic benefits and have promising implications for robotic swarms.

Abstract

Fish in schooling formations navigate complex flow fields replete with mechanical energy in the vortex wakes of their companions. Their schooling behavior has been associated with evolutionary advantages including energy savings, yet the underlying physical mechanisms remain unknown. We show that fish can improve their sustained propulsive efficiency by placing themselves in appropriate locations in the wake of other swimmers and intercepting judiciously their shed vortices. This swimming strategy leads to collective energy savings and is revealed through a combination of high-fidelity flow simulations with a deep reinforcement learning (RL) algorithm. The RL algorithm relies on a policy defined by deep, recurrent neural nets, with long–short-term memory cells, that are essential for capturing the unsteadiness of the two-way interactions between the fish and the vortical flow field. Surprisingly, we find that swimming in-line with a leader is not associated with energetic benefits for the follower. Instead, “smart swimmer(s)” place themselves at off-center positions, with respect to the axis of the leader(s) and deform their body to synchronize with the momentum of the oncoming vortices, thus enhancing their swimming efficiency at no cost to the leader(s). The results confirm that fish may harvest energy deposited in vortices and support the conjecture that swimming in formation is energetically advantageous. Moreover, this study demonstrates that deep RL can produce navigation algorithms for complex unsteady and vortical flow fields, with promising implications for energy savings in autonomous robotic swarms.

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